Electrostatically generated bubble assisted patterning at micro and nanoscale
ABSTRACT
Surface patterning at the micro and nanoscale is critical in areas like microelectronics, photonics, biosensing, and materials science. A variety of techniques have been developed to produce these patterns. The majority of these techniques are lithographic; they transfer patterns on a substrate making them highly sophisticated and complex, but inflexible. Machines are locked into a pattern size and are unable to deviate from the parameters they have been designed with.
Here we investigate if bubbles,which have long been known to cause surface pitting on metals ,ceramics and polymers, can be used to carefully and precisely pattern a substrate on nano and microscale.
Electrostatic nucleation and detonation of bubbles is evaluated as a possible technique that can satisfy stringent requirements of nucleating and collapsing nanosized bubbles. Bubble size can be modulated through electric fields giving this technique flexibility in engraving features,in a range of sizes, on a substrate that is not possible in other lithographic methods.
If successful, bubble based nano patterning could open up new cost effective routes for the production of nano confined plasmas, display panels, plasma electrolysis for hydrogen production and plasma based integrated circuits for computation.
INTRODUCTION
Bubbles are ubiquitous in nature. They play a critical role in gas exchange in natural water bodies, in evaporation of water and in heat transport. They exist in a range of sizes — micro,nano,mili and have found application in sonochemistry, surface cleaning , peening, mixing, water purification — through dissociation of organic radicals, nanofibrillation — through ultrasonic milling,plasma discharge comminution and in drug delivery among others.
Even after decades of study bubbles remain a fascinating topic of research because of their wide applicability in a range of industrial processes. Bubble research is uniquely interdisciplinary combining aspects of fluid mechanics,acoustics, thermodynamics,mechanics, physical chemistry and electrostatics.
Through sonochemistry bubbles have opened up an entirely new branch of science that is being actively developed —one that can perhaps one day unlock the gates of green chemistry at the very least for production of industrially important chemicals. Ultrafast cooling provided by bubbles is being used to develop a scalable process for fabrication of metallic glasses whereas its ability to generate intense pressure is being investigated to improve the production yield of nanomaterials. Phenomena such as sonoluminescence remains a topic of healthy debate among researchers. It seems that bubbles have found their niche in all scientific disciplines — physical,chemical,biological.
Yet despite several breakthroughs in our understanding of bubbles we have not been able to effectively utilise them and their application has been rather limited.
For example it's true that bubbles generate intense pressures when they cavitate under water. This makes them ideal for nano milling but the problem is how do you generate bubbles on the surface to be milled and collapse it with accuracy. Most bubbles simply nucleate and implode within the fluid leading to a very low efficiency despite being so effective at generating high pressures.
It is understood now that surface bubbles and bubbles within bulk behave very differently and to make them ‘do work’ requires precise control over surface properties of the material which is no easy task & most of the times too stringent a requirement for many industries such as milling.
Precise control over bubbles remains elusive. But despite all of the shortcomings bubbles do present a unique opportunity to develop new tools and techniques to process materials.
In this paper we explore a method to use bubbles to pattern surfaces of materials with micro and nano sized features. Our material of choice is aluminosilicate glass but this technique should be replicable to other ceramics.
(Metals are more difficult to pattern using this technique because they are conductive and under intense electric fields may lead to production of gasses that would disrupt control over bubbles size.)
The basic principle which enables this method to work is the well known, experimentally observed fact that when bubbles are pinned to a solid surface they collapse asymmetrically leading to a generation of a microjet that can reach supersonic speeds when it impacts the surface.
We review some of the techniques used to generate bubbles and present reasons why they are unsuitable for precise nano patterning. We then develop a technique that can be used to generate nano-micro bubbles reliably and pattern the substrate through their implosion.
Such patterned surfaces could have important applications in photonics, plasma electrolysis for hydrogen generation,nano confined plasma for display devices and plasma based electronic integrated circuits.
The motivation for developing this technique comes from the complications that modern lithographic devices suffer from. While they have been instrumental in developing the electronics industry and shaping the information age they are inflexible and highly integrated with other processes. Further the sophistication required to build these machines is beyond the reach of many nations. There is a need to develop cheap, scalable tools that can reliably develop nanosized patterns.
In contrast the technique we propose is flexible and can produce features ranging from a 100nm to a micrometer by adjusting the mechanical properties of the fluid medium — water. The inherent limitations imposed on the minimum size is not due to limitations in technique itself but due to limitations of the fluid and substrate material —specifically dielectric field strength. Further size reductions are possible if high dielectric strength fluids and substrates could be designed.
PROBLEMS WITH GENERATION OF BUBBLES THROUGH HEAT AND MECHANICAL MEANS
Industrially the two most important methods of creating bubbles are acoustic cavitation that uses high pressure sound waves to create bubbles and heat either through laser sources for localised bubble production or simply by heating the container.
In the acoustic method of generating bubbles while the size of the initial bubble is equal to the pressure applied by the wave — with the radius determined by limits set by Laplace pressure,the rectified diffusion of air in subsequent expansion and compression phases of the bubble leads to uneven size distribution of bubbles. Some stay at the Laplace radius but most grow larger to sizes that appear random due to lack of control that can be enforced by the acoustic wave.
Furthermore the inherent agitation of the fluid by the acoustic wave causes the bubble cloud to disperse making it highly difficult to control the bubble population. High bubbles velocities cause bubbles to strike against each other puncturing the bubble skin at point of contact leading to redistribution of gas and bubble growth.
Laser based tech. generates heat at a localised spot that is confined to the radius of the laser beam. It is more precise than acoustic methods but it too suffers from lack of control over the bubble size. When liquid volume is vaporised it rapidly forms vapor bubbles whose size depends upon the volume of the vapor generated which can be controlled to some extent by limiting the energy deposition by the laser.
(An unintended side effect is the production of shockwaves due to rapid vaporisation that can limit control over bubble position)
But even in these controlled setups bubbles implode violently when the vapor inside is condensed due to removal of heat. If on the other hand heat is continually supplied more vapor will form leading to expansion in the size of the bubble and its eventual popping. Like acoustic bubbles, laser bubbles are inherently unstable and difficult to control in size and position in space.
Bubbles generated due to heating a container are even less controllable as the only parameter that can be tweaked here is the temperature of the container. Heat is rarely, if ever, evenly distributed and while some sections will produce bubbles profusely others will seem inactive. Industrially, heat may be used to limit the gibbs free energy of nucleation but not to generate new bubbles.
Bubbles formed through a discharge in fluid are somewhat similar to laser produced bubbles in that they vaporise a small volume of fluid due to heat. There have been reports of nanobubbles being produced through this method but again it's difficult to control the size due to localised hotspots in the same way it's difficult to size control laser bubbles.
Bubbles are produced in large quantities during electrolysis. But due to the nature of electrochemical reactions there is profuse gas evolution near the electrodes which leads to convection. Bubbles being close to each other and moving in a rapid upswing of gas coalesce to form micro and macro bubbles. Size control is difficult and it's even more difficult to pin then down
Hydrodynamic cavitation is another method to generate bubbles in which the fluid is made to travel through a narrow neck like passage (venturi tube generally) to increase its velocity which stretches the fluid column and once its pressure is sufficiently negative bubbles nucleate. It is possible to adjust the neck diameter and thus the velocity of fluid through it but like acoustic cavitation the bubbles produced are not evenly distributed in size and are in motion with the fluid which makes their collapse rather difficult if it needs to be precisely managed.
ELECTROSTATIC GENERATION OF BUBBLES
Bubbles are produced in one of the 2 situations:
First when air comes in contact with water. Because of surface tension water forms a shell around the gas pocket leading to formation of bubbles. This is what happens when air molecules strike the water surface and penetrate to subsurface layers, during gas evolution in electrochemical reactions and even during vaporisation.
And second when it is stretched mechanically in a way that stress exceeds the tensile strength of the fluid. When that happens dissolved gas comes out of liquid and vapor molecules are formed that lead to bubble nucleation filled with gas and vapor.
Electrostatic fields give us the tool to apply electric stress to the fluid on a molecular level while keeping it stable and stationary. This differs significantly from acoustic bubble production which applies mechanical stress but agitates water or hydrodynamic production which again can't keep the water column stable.
The relevant eqn set to describe the behaviour of electrostatic forces on a fluid is given below.
The stress applied on fluid is given by the eqn 1
This term comes from maxwell stress tensor when the electric field is perpendicular to the surface and magnetic effects are ignored. The off diagonal terms (ex ExEy, EzEx) in the tensor represented by eqn 2 vanish because electric field is applied only in a single direction (Ey=Ez=0),in this case along the x axis. Its components in y and z fields are 0.
Eqn 3 represents the tensile stress on the fluid and it is this eqn that leads to the formation of bubbles due to cavitation i.e if it exceeds the tensile strength of fluid.
Eqn 4 and 5 are compressive stresses generated along the y and z direction. They don't result in cavitation.
The relevant equation set that describes the behaviour of bubble under applied stress is given below
The radius of the bubble is given by the Laplace pressure —expressed by eqn 6. The tensile stress must match (or rather slightly exceed) this pressure to produce a bubble of desired radius.
The gibbs free energy is given by eqn 7
In electrostatic application of stress the bubble growth is minimal — because the conditions conducive to growth are absent: neither is there rectified diffusion as in the case of acoustic bubble production nor is there gas supersaturation as in case of electrochemical evolution or heat induced bubbling.
The number of bubbles produced depend upon the energy supplied and once bubble saturation is reached new bubbles are not formed or come at the expense of existing bubbles.
In short, the electrostatic method of bubble production not only gives precise control over bubble size but also keeps the bubble solution stable and static. Bubbles don't grow because gas is not evolving and the solution is not in motion. Nor do they cavitate unless the applied electric field is switched off.
This method also prevents ostwald ripening from occurring because unlike other methods the bubble size distribution would be fairly uniform — due to electrostatic fields applying an unchanging pressure throughout the liquid. It is this property that separates it from other techniques where pressure distribution may be non uniform. It's difficult to control pressure in hydrodynamic or acoustic cavitation. Electric fields can be applied to large areas with precise control.
Electric fields also polarise the surface of bubbles. This keeps them arranged and imposes an order that would otherwise have been difficult to enforce. This is not much different from alignment of Liquid crystals in an electric field. Electric field alignment is used extensively in materials science like in electrospinning,polymer alignment, Electrorheological (ER) Fluids,Dielectrophoresis (DEP) of Particles.
(The polarised bubbles will attract each other as they stack vertically and repel each other as they stack horizontally the combined effect would be arrangement of bubbles in a 3D space in an orderly manner much like atoms in a crystal lattice)
Bubbles are sensitive to surface properties. So if the surface is to be patterned it would be useful to coat the surface with hydrophobic materials like oil.
CONTROL OVER PATTERN SIZE
Patterns will be formed on the substrate due to collapse of surface bubbles. Surface bubbles collapse asymmetrically leading to a microjet that impacts the wall that results in pitting.
It has been observed that pit diameter is usually equal to the diameter of the jet that strikes it which is a fraction of bubbles diameter 10-30%.
The control over pattern size is therefore provided by at least 2 tunable parameters. First is the bubble size itself. The second is the jet diameter. From experimental observations even micron size bubbles will produce nanometer patterns so there is room here. Multiple impacts can be used to produce a pit of desired size.
The impacting microjet leads to a water hammer on the surface that results in surface fracture.
Although the microjet speed is supersonic, it is only relative to the speed of sound in water. On solid surfaces like glass sound travels much faster —3 to 4K m/s so the actual impact speed is subsonic relative to the substrate. Therefore no shockwaves are produced within the material. It's only in fluid that shockwaves are produced. The shock energy is less than the energy stored inside the bubble and the collapse of the final bubble in the column deposits this energy on the substrate leading to pit formation.
DETONATION TECHNIQUES
Nanobubbles are exceptionally stable and can last from hours to months. Removal of electric fields will not collapse a nanobubble unless it's a vapor bubble. Considering that air is almost always dissolved in water and that degassing will change its mechanical properties it is important to find a way to detonate air bubbles — produced in a gaseous solution.
Several possibilities exist. Bubbles could be detonated by shockwaves created by other bubbles or plasma discharge. They could be ruptured by heating the surface or causing changes in pressure. The actual technique used would depend upon the precision required. If uniform patterning is required over the entire surface, shockwave detonation might work. But if more precision is required it may be useful to consider detonating a column of bubbles through electric field poking.
The most precise method of causing a bubble to collapse is by disturbing its liquid film. But since these bubbles are nm in size it would require extremely accurate positioning of a probe to disturb it. A more useful method would be to create a column of bubbles to a reasonable distance say 1mm from the substrate and collapse the top most bubbles using an electric field — recall that electric fields exert tensile stress on the surface of fluid
So if it exceeds the Laplace pressure of the bubble it will collapse resulting in an asymmetric jet that would collapse the rest of the bubbles in the chain.
The electric fields can be precisely controlled to nm scales ensuring that the pressure is applied only to the immediate bubble and not the adjacent chains.
This columnar implosion technique can be applied to multiple columns at once by adjusting the electric fields at column heads. This gives the operator a way to pattern the entire surface in one go rather than going block by block resulting in an exceptionally fast patterning technique.
Of course to apply this method one needs finely spaced probes with pits that are electrically accessible — this can be created using uniformly patterned substrate in which pits are spaced apart by bubble diameters. A matrix addressable scheme like those used in plasma TV to control pixels can give direct control over each pit. Simply tweaking the voltage lets you apply stress on the bubble surface and cause a rupture that propagates down the chain due to microjets that impact each subsequent bubble.
A NUMERICAL EXAMPLE DEMONSTRATING THE ENERGY REQUIRED TO COVER THE SURFACE OF IM^2 PLATE WITH BUBBLES 100nm IN RADIUS
Using eqn 7 we first calculate the Laplace pressure of the bubble of a given radius.
For 100nm bubbles this comes out to be 1.44 MPa
Then we calculate the electric field required to drop the fluid pressure below this pressure using eqn 3
This comes out to be 63.8 MV/m— note that this number is slightly lower than the breakdown strength of water 65-70MV/m
We then calculate the Gibbs free energy for a single bubble generated this way
This is 3.18 m 10^-15J
We then calculate the number of bubbles in a 1mx1m area.
3.18×10^13 bubbles.
Clearly it can be seen that less than a joule of energy will be required to nucleate these bubbles.
For these bubbles we calculate the total amount of gas present in them and compare it with relative volume of water.
A single nanobubble of 100nm radius would contain only
5.4x10^-21 moles. Calculated using ideal gas law at vapor pressure of water at 25C when it's under negative pressure (tension)
Now when 100nm bubbles cover 1mx1m of a surface it only consumes about 3.1x10^-6 g of vapor
Where as total water weight in that volume is .1 g
This shows that even with a large density of bubbles the actual weight of water trapped in them is exceedingly low.
For full paper along with refrences please view this link
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